Magnetic Superconducting Properties In Magnetic Superconductor Junctions, The Josephson Current

Recently, the observation of new superconductivity in ferromagnetic metals inexperiments, as UGe₂,ZrZn₂,URhGe and CeCoIn₅, has attracted much attentionon the coexistence of ferromagnetism and superconductivity. It has been an interest-ing subject in condensed matter physics because of their abundant and basic physics,as well as their underlying applications foreground. In this paper, we study the Zee-man effects on the s-wave superconductor and d-wave superconductor, and discussthe conditions of the coexistence of superconductivity and ferromagnetism. Also,the Josephson effects are studied in ferromagnetic superconductor tunnel junction.The main work and results are summarized as follows:Some fundamental conceptions are introduced, including the Andreev reflectionproperties in superconductor tunnel junction, Blonder-Tinkham-Klapwijk (BTK)theory in normal metal/superconductor junction, the Josephson current in super-conductor tunnel junction, and the high-T_c superconductors properties.By applying a Zeeman magnetic field to the s-wave and d-wave superconduc-tor, we solve self-consistent equations for the s-wave and d-wave superconductinggap and the magnetization in the mean-field approximation, calculate the differencein thermodynamic potential between ferromagnetic superconductivity and normalstates, and discuss the conditions of coexistence of superconductivity and ferromag-netism. It has been shown in the analysis of the coexistence condition of super-conductivity and ferromagnetism that in the case of s-wave superconductor, thezero centre-of-mass momentum Cooper pair exists at h₀＜0.707△₀₀ and the Fulde-Ferrell-Larkin-Ovchinnkov (FFLO) states exist at 0.707△₀₀＜h₀＜0.754△₀₀, where△₀₀ is the maximum energy gap at = 0, h₀ = 0.At h₀＞0.754△₀₀, the formationof Cooper pair is totally suppressed and the superconductor is destroyed. As ford-wave superconductor, at h₀＜0.56△₀₀ the zero centre-of-mass momentum Cooperpair exists, at 0.56△₀₀＜h₀＜1.06△₀₀ the FFLO states appear, and as h₀ increasesto h₀＞1.06△₀₀, the superconducting state is changed into the normal state. Meanwhile, we apply an extended Furusaki-Tsukada approach to study theJosephson effects in ferromagnetic s-wave superconductor/insulator/ferromagneticd-wave superconductor junctions. The analytic expressions for the Josephson currentin parallel and antiparallel alignments of the magnetizations in two superconductorelectrodes are obtained as a function of the temperature, exchange field, insulatingbarrier strength, and phase difference. It is shown that the Josephson currents inferromagnetic s-wave superconductor/insulator/ferromagnetic d-wave superconduc-tor junction depend on the relative orientation of the effect exchange field of the twomagnetic superconductor electrodes, and the crystal orientation of the d-wave super-conductor. The exchange energy can under certain conditions enhance the Josephsoncritical current in a ferromagnetic s-wave superconductor/insulator/ferromagneticd-wave superconductor junction.